Dot product of $$$\left\langle 6, 2\right\rangle$$$ and $$$\left\langle -4, -6\right\rangle$$$

Calculate $$$\left\langle 6, 2\right\rangle\cdot \left\langle -4, -6\right\rangle$$$.

The dot product is given by $$$\mathbf{\vec{u}}\cdot \mathbf{\vec{v}} = \sum_{i=1}^{n} u_{i} v_{i}$$$.

Thus, what we need to do is multiply the corresponding coordinates and then add up the results: $$$\left\langle 6, 2\right\rangle\cdot \left\langle -4, -6\right\rangle = \left(6\right)\cdot \left(-4\right) + \left(2\right)\cdot \left(-6\right) = -36.$$$

$$$\left\langle 6, 2\right\rangle\cdot \left\langle -4, -6\right\rangle = -36$$$A